Find which of the following matrices is an inverse to the matrix A below if any. $A = \left[ \begin{array} { c c }
- 4 & - 3 \
- 1 & 7
\end{array} \right]$ Matrix I: $\frac { 1 } { 31 } \left[ \begin{array} { c c } - 7 & - 3 \ - 1 & 4 \end{array} \right]$
Matrix II : $\frac { 1 } { 31 } \left[ \begin{array} { c c } 4 & 3 \ 1 & - 7 \end{array} \right]$
Matrix III : $\frac { 1 } { 31 } \left[ \begin{array} { c c } 7 & - 3 \ - 1 & - 4 \end{array} \right]$
A)Each of the matrices I and II is an inverse of A.
B)Each of the matrices I and III is an inverse of A.
C)Matrix II is an inverse of A.
D)Matrix I is an inverse of A.
E)None of the matrices is an inverse of A.

Question

Find which of the following matrices is an inverse to the matrix A below if any. $A = \left[ \begin{array} { c c } 
- 4 & - 3 \
- 1 & 7
\end{array} \right]$ Matrix I: $\frac { 1 } { 31 } \left[ \begin{array} { c c } - 7 & - 3 \ - 1 & 4 \end{array} \right]$
Matrix II : $\frac { 1 } { 31 } \left[ \begin{array} { c c } 4 & 3 \ 1 & - 7 \end{array} \right]$
Matrix III : $\frac { 1 } { 31 } \left[ \begin{array} { c c } 7 & - 3 \ - 1 & - 4 \end{array} \right]$
A)Each of the matrices I and II is an inverse of A.
B)Each of the matrices I and III is an inverse of A.
C)Matrix II is an inverse of A.
D)Matrix I is an inverse of A.
E)None of the matrices is an inverse of A.

Quizplus · Accepted Answer

Matrix I is the inverse of A because $AA^{-1} = A^{-1}A = I$, where I is the identity matrix.

Find Which of the Following Matrices Is an Inverse to the Matrix